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public static double evaluate(String expression) {
        Deque<Double> operands = new ArrayDeque<>();
        Deque<Character> operators = new ArrayDeque<>();
    
        for (int i = 0; i < expression.length(); i++) {
            char c = expression.charAt(i);
            if (Character.isDigit(c)) {
                // Parse the number and push it to the operand stack
                int j = i;
                while (j < expression.length() && (Character.isDigit(expression.charAt(j)) || expression.charAt(j) == '.')) {
                    j++;
                }
                double num = Double.parseDouble(expression.substring(i, j));
                operands.push(num);
                i = j - 1;
            } else if (c == '+' || c == '-' || c == '*' || c == '/' || c == '^' || c == '(') {
                // Push the operator to the operator stack
                operators.push(c);
            } else if (c == ')') {
                // Pop operators and operands until we reach the matching '('
                while (!operators.isEmpty() && operators.peek() != '(') {
                    char op = operators.pop();
                    double b = operands.pop();
                    double a = operands.pop();
                    double result = applyOperator( a, b, op);
                    operands.push(result);
                }
                if (!operators.isEmpty() && operators.peek() == '(') {
                    operators.pop(); // Discard the '('
                }
            } else if (c == ' ') {
                // Ignore whitespace
            } else {
                throw new IllegalArgumentException("Invalid operator: " + c);
            }
    
            // Check if we need to perform multiplication
            if (i < expression.length() - 1 && (c == ')' || Character.isDigit(c)) && (expression.charAt(i + 1) == '(' || expression.charAt(i + 1) == '.' || Character.isDigit(expression.charAt(i + 1)))) {
                // We need to perform multiplication, so push a '*' operator to the operator stack
                operators.push('*');
            }
        }
    
        // Perform any remaining operations
        while (!operators.isEmpty()) {
            char op = operators.pop();
            double b = operands.pop();
            double a = operands.pop();
            double result = applyOperator( a, b, op);
            operands.push(result);
        }
    
        return operands.pop();
    }